### Graphical and Algebraic Synthesis for PWM Methods

S.L. Capitaneanu, B. de Fornel, M. Fadel, J. Faucher, A. Almeida
2001 EPE Journal
The article proposes an algebraic synthesis for PWM methods, which is based on a graphical representation of the 2 levels VSI (Voltage Source Inverter). This theory can be the starting point for every PWM method representation. In order to understand the historical evolution of the PWM methods the authors propose two classification groups of the main PWM techniques. The main classification is based on the movement of the neutral point (zero-voltage V N0 evolution). The details of PWM methods
more » ... s of PWM methods presented here are also seen from the graphical representation perspective. The equivalence between the well-known SVM (Space Vector Modulation) practically DDT realized (Direct Digital Technique) and the three-phase PWM with a carrier based industrial realization is shown. The principles of the three-phase PWM and the 3 rd harmonic injection PWM (THIPWM4, THIPWM6) are compared the same as the DPWM (Discontinuous PWM) methods. These classifications and equivalences between different techniques show that the number of contemporary used PWM principles can be reduced. The general complex space representation and the classifications proposed here are simple to comprehension educational tools and they simply the way towards practical implementation. GLOSSARY a i , i=1,2,3: inverter duty cycles i α , i=0,...,7: inverter voltages application times Ci, i=1,...,6: inverter IGBTs E=bus voltage f m : frequency of the reference wave (modulation wave) f PWM : PWM switching frequency m a : modulation amplitude m i : modulation index Sci, i=1,2,3 : inverter orders for the 6 switches T e : sampling period Ti[k], i=1,2,3: pulse width at k sampling instant V i0 , i=1,2,3: inverter line voltage V iN , i=1,2,3: motor line voltage from supplying point of view (fig.1) V iref , i=1,2,3: inverter reference voltages V medium : medium voltage as in fig.23 V N0 : zero-voltage or zero-sequence signal (fig.1) V PWM : fundamental of the reference voltage when using PWM method V ref : inverter reference voltage in complex representation V six-step : fundamental of reference voltage when using six-step wave V s : motor voltage in complex representation DDT: direct digital technique (for PWM implantation) [2], [7] THIPWM4 or 6: PWM with 3 rd harmonic injection [3], [6] Three-phase PWM: PWM with V medium injection with modulation wave/triangular carrier implantation [4], [5], [23] VSI: Voltage Source Inverter Let the IGBTs be C1, C2...C6 and the on/off orders of the 6 switches be Sc1, Sc2, ..., Sc6 (positive logic) :